在二冪策略下考量數量折扣的合併補貨問題之研究

Abstract

合併補貨問題(Joint Replenishment Problem, JRP)藉由決定各產品之補貨週期、補貨數量與補貨次數，使平均總成本最小化。本研究將探討在二冪策略下考量數量折扣的合併補貨問題(Joint Replenishment Problem with Quantity Discount under Power-of-Two policies, JRPQD-PoT)，由於數量折扣的因素，使得產品採購成本並非為常數，因此除了考量傳統JRP問題中的成本項，還需增加產品採購成本。本研究將提出JRPQD-PoT數學模式，並且使用圖形方法呈現JRPQD-PoT之目標函數結構，進行完整的理論分析。利用這些理論分析發展出一套有效的搜尋演算法，以尋找在二冪策略下考量數量折扣之合併補貨問題的全域最佳解。本研究將在隨機數據實驗進行本研究演算法與二冪策略下傳統JRP問題求解方法求解品質之比較，以隨機數據實驗證明本研究所發展之求解JRPQD-PoT演算法為一優良的求解方法。

The joint replenishment problem (JRP) determines the replenishment cycle time and lot size of each item so as to minimize the total costs per unit time. In this study, we consider the joint replenishment problem with quantity discount under power-of-two policies (JRPQD-PoT). Because of the quantity discount, the purchasing cost isn’t constant any more. The objective of the JRPQD-PoT is to minimize the total costs incurred per unit time. The costs considered generally include setup costs, inventory holding costs and purchasing cost. In this study, we propose the JRPQD-PoT model, perform theoretical analysis and derive a global optimum search algorithm for the joint replenishment problem with quantity discount under power-of-two policies. Evidently, we provide a numerical example to demonstrate the efficiency of the proposed algorithm.